"No rock is sentient. Some mammals are sentient. Hence, no mammal is a rock." I wrote a form and it's apparently wrong, but I don't get how.
Suppose that there is a Mammal (call it a) that is also a Rock.
By first premises, a is not Sentient.
Thus, a is a Mammal that is not Sentient.
But this does not contradict the second premise, that states that some (not necessarily all) Mammals are Sentient .
The logical form is:
No Rock is Sentient --- ¬∃x(Roc(x) and Sen(x))
Some mammals are sentient --- ∃x(Mam(x) and Sen(x))
Therefore: No mammal is a rock --- ¬∃x(Mam(x) and Roc(X)).
"No rock is sentient. Some mammals are sentient. Hence, no mammal is a rock."
X = rocks
Y = sentient things
Z = mammals
No X are Z. Some Y are Z. Therefore, no Z are X.
Euler diagram looks like this:
╭─rocks─────╮ ╭─sentient things───╮ │ │ │ │ │ ╭─────┼─────┼────╮ │ ╰─────┼─────╯ ╰────┼──────────────╯ │ │ ╰──mammals───────╯
The "rocks" bubble and the "sentient things" bubble do not intersect as provided by the first premise. The "mammals" bubble intersects with the "sentient things" bubble as provided by the second premise. Nothing in the two premises says anything about whether the "mammals" bubble intersects the "rocks" bubble, so it may, making the conclusion invalid.
Suppose there are just two Mammals, one is a rock and the other is sentient, this satisfy the first two propositions, but contradicts your conclusion. If you read "thinking fast and slow" a great book by Daniel Kahneman, you would always want to Try and change the arguments into humanly relatable statements, an example of changing the arguments above and make it simpler to understand is :
No babies are quantum-physicists, some humans are quantum-physicists. now the conclusion " No humans are babies " is easily rejected.